Segmentation of a structure

ABSTRACT

A method and a segmentation system are disclosed. An embodiment of the method includes providing an image representation of the structure; providing a start surface model, including a mesh with a plurality of vertices connected by edges; defining for each vertex a ray normal to the surface model at the position of the vertex; assigning more than two labels to each vertex, each label representing a candidate position of the vertex on the ray; providing a representation of likelihoods for each candidate position the likelihood referring to whether the candidate position corresponds to a surface point of the structure in the image representation; and defining a first order Markow Random Field with discrete multivariate random variables, the random variables including the labels of the candidate positions and the representation of likelihoods, finding an optimal segmentation of the structure by using an maximum a posteriori estimation in this Markow Random Field.

PRIORITY STATEMENT

The present application hereby claims priority under 35 U.S.C. §119 toU.S. patent application No. 61/829,661 filed May 31, 2013, the entirecontents of which are hereby incorporated herein by reference.

FIELD

At least one embodiment of the present invention generally relates to amethod for segmentation of a structure, in image data. At least oneembodiment of the present invention also generally relates to asegmentation system for that purpose.

An embodiment of the below-described method may generally be used forsegmentation of any arbitrary structure in image data, in particular inmedical image data such as tomographic image data. A “structure” maythus be generally any object with a bounding surface. A first examplefrom non-medical image data can be considered to involve a segmentationof an object within a larger object, for instance a garment, a bottle orwhatever other object in a closed suitcase of which inner image data aretaken, e.g. by X-ray.

In medical image data, i.e. image data of a living or dead being (humanor animal), structures may in particular refer to organs such as bloodvessels or the heart (any many other well-known organs of the body of aliving) but also to other structures such as tissue structures, bonestructures or the like. Throughout the description below reference ismade to blood vessels as a particularly prominent example, which howeverdoes not limit the overall scope and applicability of the embodiments ofthe invention to that purely example application.

BACKGROUND

According to the American Heart Association, coronary artery disease(CAD) is a leading cause of death in the western world. The currentdiagnostic standard for CAD is conventional invasive angiography (ICA),which involves a considerable amount of risk and cost. New generationsof cardiac computed tomography (CT) scanners enable the acquisition ofCoronary CT Angiography (CCTA) images with unprecedented quality.Coronary stenoses can be detected with high sensitivity in CCTA whichallows that method to be used as a gatekeeper to invasive diagnostic andsurgical procedures such as ICA.

Methods for the automatic detection of coronary stenoses in CCTA havebeen proposed for clinical trials. Recently, CCTA has also been proposedfor the simulation of pressure distributions along coronary stenoses andfor the computation of the so-called fractional flow reserve (FFR) whichis indicative for ischemia-causing lesions. Both an automatic detectionof coronary stenoses as well as the simulation of their hemodynamicrelevance (i.e. the simulation-based detection of pressure drops withinthe coronary vessels) rely on accurate segmentation of the coronarylumen in the image data provided. This is a challenging task as coronaryvessels are comparatively small (extending to only a few voxels in imagedata in their distal parts) whereas CCTA image volumes are of varyingquality (in particular with relation to noise, artifacts, contrasthomogenity etc.). Accurate segmentation is further complicated as thecontrast of the vessel lumen is only slightly higher than that ofnon-calcified plaques but lower than that of calcified plaques.Therefore, non-calcified plaques appear optically very similar to thebackground of the vessel, in particular in a contrast-enhanced imageacquisition process. On the other hand, calcified plaques appear to bepart of the lumen of the vessel in such contrast-enhanced imageacquisition processes as they show about the same appearance as thecontrast agent in the image data. Therefore, a distinction betweencalcified plaque and lumen of the blood vessel through which blood canflow is very difficult to make.

This explanation shows how important an accurate segmentation ofstructures can be in the context of the advancement of methodologies ofautomatic evaluation of illnesses. While numerous segmentation methodsfor structures in image data do exist already, there still remains theneed for particularly accurate segmentation methods and algorithms.

SUMMARY

At least one embodiment of the present invention provides analternative, preferably improved segmentation method, in particular withreference to blood vessels, but not restricted to the purpose.

A method and a segmentation system are disclosed.

According to at least one embodiment, a method comprises:

a) providing an image representation of the structure. Such imagerepresentation may for instance comprise the image data, but also arepresentation thereof (or both) such as a vesseltree of a (blood)vessel.

b) providing a start surface model, comprising a mesh with a pluralityof vertices connected by edges, preferably undirected edges. Such startsurface model may already exist before or be computed in the context ofthe method according to an embodiment of the invention.c) defining for each vertex of the plurality of vertices a ray normal tothe surface model at the position of the (corresponding) vertex.d) assigning more than two (for instance five) labels to each vertex,each label representing a candidate position of the vertex on the ray.Each of such labels thus corresponds to one candidate position andcharacterizes that candidate position for instance by indicating a rankof that candidate position along the ray.e) providing a representation of likelihoods for each candidate positionthe likelihood referring to whether the candidate position correspondsto a surface point of the structure in the image representation. In thiscontext, the labels of the candidate positions can be used.f) defining a first order Markow Random Field with discrete multivariaterandom variables, the random variables comprising the labels of thecandidate positions and the representation of likelihoods.g) finding, i.e. searching and/or identifying an optimal segmentation(such as a segmentation model and/or segmentation mesh) of the structureby using a maximum a posteriori estimation in this Markow Random Field.Thereby, an optimal segmentation is characterized by the fact that thesegmentation has a maximum likelihood that the segmentation modelrepresents a true surface of the structure.

According to an embodiment of the invention, a segmentation systemcomprises:

a) a first provision unit realized to provide an image representation ofthe structure. This first provision unit corresponds in function withstep a) of the method according to an embodiment of the invention. Itmay be realized as a computation unit which in operation computes theimage representation, but may also comprise an input interface forreceiving such image representations from other units or modalitiesoutwith (or within) the segmentation system.b) a second provision unit, which may also be comprised by the firstprovision unit to form a common provision unit, realized to provide astart surface model, comprising a mesh with a plurality of verticesconnected by edges. This second provision unit corresponds in functionwith step b) of the method according to the invention. It may also berealized as a computation unit which in operation computes the startsurface model or again comprise an input interface realized to receivethe start surface model from other units or modalities outwith (orwithin) the segmentation system.c) a definition unit which in operation defines for each vertex a raynormal to the surface model at the position of the vertex. Thisdefinition unit corresponds in function with step c) of the methodaccording to an embodiment of the invention.d) an assignment unit realized to assign more than two labels to eachvertex, each label representing a candidate position of the vertex onthe ray. This assignment unit corresponds in function with step d) ofthe method according to an embodiment of the invention.e) a third provision unit which in operation provides a representationof likelihoods for each candidate position the likelihood referring towhether the candidate position corresponds to a surface point of thestructure in the image representation. The third provision unit, whichis preferably realized as a computation unit which in operation computesthe representation of likelihoods. It corresponds in function with stepe) of the method according to an embodiment of the invention.f) a definition unit which in operation defines a first order MarkowRandom Field with discrete multivariate random variables, the randomvariables comprising the labels of the candidate positions and therepresentation of likelihoods. The definition unit corresponds infunction with step f) of the method according to an embodiment of theinvention.g) a finding unit realized to find an optimal segmentation of thestructure by using an maximum a posteriori estimation in this MarkowRandom Field. The finding unit corresponds in function with step g) ofthe method according to an embodiment of the invention.

The segmentation system according to an embodiment of the invention,and/or the determination assembly according to an embodiment of theinvention, in particular its first and/or second and/or third provisionunits, the definition unit, the assignment unit, the definition unit,and the finding unit (but also other components of the segmentationsystem which are mentioned below) may be partially or whollyaccomplished by hardware components, for example using semiconductorchips such as ASICs (Application Specific Integrated Circuits), FPGAs(Field Programmable Gate Arrays), or PLAs (Programmable Logic Arrays).They may, however, also be comprised of software components orcombinations of hardware and software components. Therefore, anembodiment of the invention also concerns a computer programme productcomputer programme product directly loadable into a processor of aprogrammable segmentation system comprising programme code segments toconduct all steps of a method according to an embodiment of theinvention when the computer programme product is executed on thesegmentation system.

It is further preferred that the likelihood function part is based on apre-given boundary likelihood of the image representation of thestructure provided in step a). Such boundary likelihood can be derivedusing all different kinds of likelihood determination algorithms such asfunctions of image gradients. A preferred one is obtained from a trainedboundary classifier. A particularly preferred one in the context of thesegmentation of blood vessels comprises a method whereby the boundarylikelihood is a corrected boundary likelihood derived by the steps of:

-   -   providing a vesseltree representation of the blood vessel,    -   providing a number of preliminary boundary likelihoods of a        number of cross-sections of the blood vessel,    -   providing a number of intensity profiles in the image data in        the number of cross-sections,    -   determining a calcification in the cross-section based on the        intensity profile,    -   correcting each prelimiary boundary likelihood into the        corrected boundary likelihood which excludes the calcification        from an inner part of the blood vessel.

BRIEF DESCRIPTION OF THE DRAWINGS

Other objects and features of the present invention will become apparentfrom the following detailed descriptions considered in conjunction withthe accompanying drawings. It is to be understood, however, that thedrawings are designed solely for the purposes of illustration and not asa definition of the limits of the invention. They are not necessarilydrawn to scale.

FIG. 1 shows a schematic block diagramme of a segmentation processaccording to an embodiment of the invention,

FIG. 2 shows a section view of a blood vessel structure and aprogression line thereof in the course of a correction of theprogression line according to a step of the process of FIG. 1,

FIG. 3 schematically shows different steps of a warping step of theprocess of FIG. 1,

FIG. 4 shows a tubular coordinate system which can be used in thecontext of the process of FIG. 1,

FIG. 5 shows a schematic representation of a slice within the coordinatesystem of FIG. 4,

FIG. 6 shows a schematic depiction of the construction of a boundary mapin the context of the process of FIG. 1,

FIG. 7 shows a schematic representation of a feature extraction processin the context of the process of FIG. 1,

FIG. 8 shows two images of a cross-section of a blood vessel with anannotated boundary map which can be used in the context of the processof FIG. 1,

FIG. 9 shows a cross-sectional image of a blood vessel withcorresponding first curves for the detection of calcified plaque in thecontext of the process of FIG. 1,

FIG. 10 shows the same cross-sectional image of the blood vessel withcorresponding second curves for the detection of calcified plaque in thecontext of the process of FIG. 1,

FIG. 11 shows an MRF representation of a blood vessel for use in thecontext of the process of FIG. 1,

FIG. 12 shows three result curves of convex functions which functionscan be used alternatively in the context of the process of FIG. 1,

FIG. 13 shows a constructed graph for max-flow analysis in the contextof the process of FIG. 1.

DETAILED DESCRIPTION OF THE EXAMPLE EMBODIMENTS

Various example embodiments will now be described more fully withreference to the accompanying drawings in which only some exampleembodiments are shown. Specific structural and functional detailsdisclosed herein are merely representative for purposes of describingexample embodiments. The present invention, however, may be embodied inmany alternate forms and should not be construed as limited to only theexample embodiments set forth herein.

Accordingly, while example embodiments of the invention are capable ofvarious modifications and alternative forms, embodiments thereof areshown by way of example in the drawings and will herein be described indetail. It should be understood, however, that there is no intent tolimit example embodiments of the present invention to the particularforms disclosed. On the contrary, example embodiments are to cover allmodifications, equivalents, and alternatives falling within the scope ofthe invention. Like numbers refer to like elements throughout thedescription of the figures.

Before discussing example embodiments in more detail, it is noted thatsome example embodiments are described as processes or methods depictedas flowcharts. Although the flowcharts describe the operations assequential processes, many of the operations may be performed inparallel, concurrently or simultaneously. In addition, the order ofoperations may be re-arranged. The processes may be terminated whentheir operations are completed, but may also have additional steps notincluded in the figure. The processes may correspond to methods,functions, procedures, subroutines, subprograms, etc.

Methods discussed below, some of which are illustrated by the flowcharts, may be implemented by hardware, software, firmware, middleware,microcode, hardware description languages, or any combination thereof.When implemented in software, firmware, middleware or microcode, theprogram code or code segments to perform the necessary tasks will bestored in a machine or computer readable medium such as a storage mediumor non-transitory computer readable medium. A processor(s) will performthe necessary tasks.

Specific structural and functional details disclosed herein are merelyrepresentative for purposes of describing example embodiments of thepresent invention. This invention may, however, be embodied in manyalternate forms and should not be construed as limited to only theembodiments set forth herein.

It will be understood that, although the terms first, second, etc. maybe used herein to describe various elements, these elements should notbe limited by these terms. These terms are only used to distinguish oneelement from another. For example, a first element could be termed asecond element, and, similarly, a second element could be termed a firstelement, without departing from the scope of example embodiments of thepresent invention. As used herein, the term “and/or,” includes any andall combinations of one or more of the associated listed items.

It will be understood that when an element is referred to as being“connected,” or “coupled,” to another element, it can be directlyconnected or coupled to the other element or intervening elements may bepresent. In contrast, when an element is referred to as being “directlyconnected,” or “directly coupled,” to another element, there are nointervening elements present. Other words used to describe therelationship between elements should be interpreted in a like fashion(e.g., “between,” versus “directly between,” “adjacent,” versus“directly adjacent,” etc.).

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of exampleembodiments of the invention. As used herein, the singular forms “a,”“an,” and “the,” are intended to include the plural forms as well,unless the context clearly indicates otherwise. As used herein, theterms “and/or” and “at least one of” include any and all combinations ofone or more of the associated listed items. It will be furtherunderstood that the terms “comprises,” “comprising,” “includes,” and/or“including,” when used herein, specify the presence of stated features,integers, steps, operations, elements, and/or components, but do notpreclude the presence or addition of one or more other features,integers, steps, operations, elements, components, and/or groupsthereof.

It should also be noted that in some alternative implementations, thefunctions/acts noted may occur out of the order noted in the figures.For example, two figures shown in succession may in fact be executedsubstantially concurrently or may sometimes be executed in the reverseorder, depending upon the functionality/acts involved.

Unless otherwise defined, all terms (including technical and scientificterms) used herein have the same meaning as commonly understood by oneof ordinary skill in the art to which example embodiments belong. Itwill be further understood that terms, e.g., those defined in commonlyused dictionaries, should be interpreted as having a meaning that isconsistent with their meaning in the context of the relevant art andwill not be interpreted in an idealized or overly formal sense unlessexpressly so defined herein.

Portions of the example embodiments and corresponding detaileddescription may be presented in terms of software, or algorithms andsymbolic representations of operation on data bits within a computermemory. These descriptions and representations are the ones by whichthose of ordinary skill in the art effectively convey the substance oftheir work to others of ordinary skill in the art. An algorithm, as theterm is used here, and as it is used generally, is conceived to be aself-consistent sequence of steps leading to a desired result. The stepsare those requiring physical manipulations of physical quantities.Usually, though not necessarily, these quantities take the form ofoptical, electrical, or magnetic signals capable of being stored,transferred, combined, compared, and otherwise manipulated. It hasproven convenient at times, principally for reasons of common usage, torefer to these signals as bits, values, elements, symbols, characters,terms, numbers, or the like.

In the following description, illustrative embodiments may be describedwith reference to acts and symbolic representations of operations (e.g.,in the form of flowcharts) that may be implemented as program modules orfunctional processes include routines, programs, objects, components,data structures, etc., that perform particular tasks or implementparticular abstract data types and may be implemented using existinghardware at existing network elements. Such existing hardware mayinclude one or more Central Processing Units (CPUs), digital signalprocessors (DSPs), application-specific-integrated-circuits, fieldprogrammable gate arrays (FPGAs) computers or the like.

Note also that the software implemented aspects of the exampleembodiments may be typically encoded on some form of program storagemedium or implemented over some type of transmission medium. The programstorage medium (e.g., non-transitory storage medium) may be magnetic(e.g., a floppy disk or a hard drive) or optical (e.g., a compact diskread only memory, or “CD ROM”), and may be read only or random access.Similarly, the transmission medium may be twisted wire pairs, coaxialcable, optical fiber, or some other suitable transmission medium knownto the art. The example embodiments not limited by these aspects of anygiven implementation.

It should be borne in mind, however, that all of these and similar termsare to be associated with the appropriate physical quantities and aremerely convenient labels applied to these quantities. Unlessspecifically stated otherwise, or as is apparent from the discussion,terms such as “processing” or “computing” or “calculating” or“determining” of “displaying” or the like, refer to the action andprocesses of a computer system, or similar electronic computingdevice/hardware, that manipulates and transforms data represented asphysical, electronic quantities within the computer system's registersand memories into other data similarly represented as physicalquantities within the computer system memories or registers or othersuch information storage, transmission or display devices.

Spatially relative terms, such as “beneath”, “below”, “lower”, “above”,“upper”, and the like, may be used herein for ease of description todescribe one element or feature's relationship to another element(s) orfeature(s) as illustrated in the figures. It will be understood that thespatially relative terms are intended to encompass differentorientations of the device in use or operation in addition to theorientation depicted in the figures. For example, if the device in thefigures is turned over, elements described as “below” or “beneath” otherelements or features would then be oriented “above” the other elementsor features. Thus, term such as “below” can encompass both anorientation of above and below. The device may be otherwise oriented(rotated 90 degrees or at other orientations) and the spatially relativedescriptors used herein are interpreted accordingly.

Although the terms first, second, etc. may be used herein to describevarious elements, components, regions, layers and/or sections, it shouldbe understood that these elements, components, regions, layers and/orsections should not be limited by these terms. These terms are used onlyto distinguish one element, component, region, layer, or section fromanother region, layer, or section. Thus, a first element, component,region, layer, or section discussed below could be termed a secondelement, component, region, layer, or section without departing from theteachings of the present invention.

According to at least one embodiment, a method comprises:

a) providing an image representation of the structure. Such imagerepresentation may for instance comprise the image data, but also arepresentation thereof (or both) such as a vesseltree of a (blood)vessel.

b) providing a start surface model, comprising a mesh with a pluralityof vertices connected by edges, preferably undirected edges. Such startsurface model may already exist before or be computed in the context ofthe method according to an embodiment of the invention.c) defining for each vertex of the plurality of vertices a ray normal tothe surface model at the position of the (corresponding) vertex.d) assigning more than two (for instance five) labels to each vertex,each label representing a candidate position of the vertex on the ray.Each of such labels thus corresponds to one candidate position andcharacterizes that candidate position for instance by indicating a rankof that candidate position along the ray.e) providing a representation of likelihoods for each candidate positionthe likelihood referring to whether the candidate position correspondsto a surface point of the structure in the image representation. In thiscontext, the labels of the candidate positions can be used.f) defining a first order Markow Random Field with discrete multivariaterandom variables, the random variables comprising the labels of thecandidate positions and the representation of likelihoods.g) finding, i.e. searching and/or identifying an optimal segmentation(such as a segmentation model and/or segmentation mesh) of the structureby using a maximum a posteriori estimation in this Markow Random Field.Thereby, an optimal segmentation is characterized by the fact that thesegmentation has a maximum likelihood that the segmentation modelrepresents a true surface of the structure.

In this context, the term “structure” refers in particular to an organ,preferably a tubular (hollow) organ, most preferred to a blood vessel.The image data are preferably tomographic image data.

According to an embodiment of the invention, a segmentation systemcomprises:

a) a first provision unit realized to provide an image representation ofthe structure. This first provision unit corresponds in function withstep a) of the method according to an embodiment of the invention. Itmay be realized as a computation unit which in operation computes theimage representation, but may also comprise an input interface forreceiving such image representations from other units or modalitiesoutwith (or within) the segmentation system.b) a second provision unit, which may also be comprised by the firstprovision unit to form a common provision unit, realized to provide astart surface model, comprising a mesh with a plurality of verticesconnected by edges. This second provision unit corresponds in functionwith step b) of the method according to the invention. It may also berealized as a computation unit which in operation computes the startsurface model or again comprise an input interface realized to receivethe start surface model from other units or modalities outwith (orwithin) the segmentation system.c) a definition unit which in operation defines for each vertex a raynormal to the surface model at the position of the vertex. Thisdefinition unit corresponds in function with step c) of the methodaccording to an embodiment of the invention.d) an assignment unit realized to assign more than two labels to eachvertex, each label representing a candidate position of the vertex onthe ray. This assignment unit corresponds in function with step d) ofthe method according to an embodiment of the invention.e) a third provision unit which in operation provides a representationof likelihoods for each candidate position the likelihood referring towhether the candidate position corresponds to a surface point of thestructure in the image representation. The third provision unit, whichis preferably realized as a computation unit which in operation computesthe representation of likelihoods. It corresponds in function with stepe) of the method according to an embodiment of the invention.f) a definition unit which in operation defines a first order MarkowRandom Field with discrete multivariate random variables, the randomvariables comprising the labels of the candidate positions and therepresentation of likelihoods. The definition unit corresponds infunction with step f) of the method according to an embodiment of theinvention.g) a finding unit realized to find an optimal segmentation of thestructure by using an maximum a posteriori estimation in this MarkowRandom Field. The finding unit corresponds in function with step g) ofthe method according to an embodiment of the invention.

Further, an embodiment of the invention concerns an imaging device withan acquisition unit and a segmentation system according to an embodimentof the invention.

The segmentation system according to an embodiment of the invention,and/or the determination assembly according to an embodiment of theinvention, in particular its first and/or second and/or third provisionunits, the definition unit, the assignment unit, the definition unit,and the finding unit (but also other components of the segmentationsystem which are mentioned below) may be partially or whollyaccomplished by hardware components, for example using semiconductorchips such as ASICs (Application Specific Integrated Circuits), FPGAs(Field Programmable Gate Arrays), or PLAs (Programmable Logic Arrays).They may, however, also be comprised of software components orcombinations of hardware and software components. Therefore, anembodiment of the invention also concerns a computer programme productcomputer programme product directly loadable into a processor of aprogrammable segmentation system comprising programme code segments toconduct all steps of a method according to an embodiment of theinvention when the computer programme product is executed on thesegmentation system.

Particularly advantageous embodiments and features of the invention aregiven by the dependent claims, as revealed in the following description.Features of different claim categories may be combined as appropriate togive further embodiments not described herein.

Preferably, a max-flow algorithm—also known under the namemax-flow/min-cut algorithm—is used in the maximum a posterioriestimation.

Further, it is preferred that a multi-label energy function is minimizedfor the maximum a posteriori estimation. In this context, it isparticularly preferred that the multi-label energy function comprises alikelihood function part (preferably a summand in the multi-label energyfunction) representing a sum of all likelihoods for the differentvertices and their labels of their candidate positions and/or that themulti-label energy function comprises a smoothness function part (e.g.again a summand) representing a smoothness of the segmentation (inparticular of a mesh model). Thereby, the smoothness function partcomprises a sum, for all edges, over function values of a convexfunction, which convex function depends on a label difference of the (inparticular neighbouring) labels connected by each edge.

Such smoothness function part preferably comprises an edge dependentweighting factor. Such edge dependent weighting factor thus depends onthe edge(s) and in particular on a length of an edge, i.e. on a distancebetween those vertices which are interconnected by the edge and/or whichdepends on a type of the edge. For instance, when the edge can beconsidered to be within a structure to be segmented, other weightingfactors can be assigned to it than if it is considered to be alignedalong the surface of the structure, in particular of a blood vessel.

It is further preferred that the likelihood function part is based on apre-given boundary likelihood of the image representation of thestructure provided in step a). Such boundary likelihood can be derivedusing all different kinds of likelihood determination algorithms such asfunctions of image gradients. A preferred one is obtained from a trainedboundary classifier. A particularly preferred one in the context of thesegmentation of blood vessels comprises a method whereby the boundarylikelihood is a corrected boundary likelihood derived by the steps of:

-   -   providing a vesseltree representation of the blood vessel,    -   providing a number of preliminary boundary likelihoods of a        number of cross-sections of the blood vessel,    -   providing a number of intensity profiles in the image data in        the number of cross-sections,    -   determining a calcification in the cross-section based on the        intensity profile,    -   correcting each prelimiary boundary likelihood into the        corrected boundary likelihood which excludes the calcification        from an inner part of the blood vessel.

Such a method thus provides for a refined boundary likelihood whichtakes into consideration calcifications within the blood vessel.

The complete example shown by way of the following figures refers to asegmentation of a calcified blood vessel or vesseltree. It is, however,to be understood that the segmentation of different structures, alsooutwith the medical imaging field, can be carried out using parts of themethodology outlined here. In particular, the calcium exclusion stepscertainly only refer to the segmentation of blood vessels, as well asfor instance the references to a progession line, especially centerline(which only refers to tubular objects).

The lumen segmentation framework shown here is performed in multiplestages which produce a mesh representation of the lumen surface in apipe-line like manner. FIG. 1 gives an overview of the framework andvisualizes the main control and data flow.

The segmentation Z starts at a starting point Y and has a first step Xin which volume data ID, i.e. image data ID and a (for instancepreviously tracked) vesseltree VT serve as input, whereas the segmentedcoronary arteries—in a mesh representation i.e. mesh segmentationcomprising mesh segmentation data MSD—form the output of this frameworkat an end point S.

Firstly, the algorithm's input data ID, VT, CVT are preprocessed in afirst—optional—vesseltree (in particular centerline) correction step X(which results in a corrected vesseltree CVT) and in a volume warpingstep W from which there result warped volume data WID. Then, potentiallumen wall boundaries are detected in a boundary detection step V alongcylindrical coordinates and stored in a boundary map BM. In order toexclude calcified regions from the segmentation, the map is analyzed instep U for the presence of calcium and modified if necessary—whichresults in a modified boundary map MBM.

At last, in step T, the final segmentation is found by embedding theboundary map as an optimization problem into a multilabel Markov RandomField with convex pair potentials and then solving it by utilizing astandard max-flow/min-cutalgorithm. Thereby, the term volume(image—image data) is used interchangeably with volumetric data.

Step X: Vesseltree Correction

The correction of the vesseltree generally concerns the correction ofits progression line, more particularly its centerline, which is shownwith reference to FIG. 2:

The lumen segmentation quality highly depends on the accuracy of theextracted vesseltree progression line of the blood vessel 1, here acenterline 3 (left). Such centerline 3 can be computed using anyavailable progression line (centerline) generating algorithm of whichthere are numerous available.

The overall segmentation algorithm of this example includes thecenterline points in the final lumen segmentation result by default.This is due to the ray-casting method (cf. below) that samples potentialboundary positions at radial distances from the centerline point. In anideal case the extracted vesseltree would always travel along points atthe center of the lumen. In practice though, the extracted vesseltree ofcoronary arteries can lack accuracy and branch falsely, especially atregions with plaque 5 and severe occlusions. Furthermore, at furcations7 it is possible that the centerline 3 follows a short-cut rather thereal lumen position (cf. FIG. 2 left). A repositioning of the pointsthat assemble the vesseltree (cf. FIG. 2 right) can ensure that thecorrected centerline 3′ runs always distant from the lumen wall, even inthe presence of severe lesions. The centerline correction X can beperformed with methods provided by Zheng et al.: Model-Given CenterlineExtraction for Severely Occluded Major Coronary Arteries. In: MachineLearning in Medical Imaging. 2012. pp. 10 to 18. The algorithm in thisreference also provides an estimate of the lumen intensity distribution(or lumen likelihood). This allows for any image voxel of the image datato map from its intensity to the likelihood of being within the vessellumen.

As a result of the vesseltree correction step X the corrected centerline3′ (at least roughly—i.e. approximately) goes through the lumen centreof the blood vessel 1 and avoids to hit calcified plaques 3.

Step W: Volume Warping

Step W is explained with reference to FIG. 3. Thereby, a warped andresampled version of the volumetric input image data ID is generated.

Since the lumen boundary of the blood vessel 1 has to be determinedexactly at those parts of the volume of the image data ID where theextracted centerline 3, 3′ runs, a particular focus is given to thoseregions in particular. These regions are determined by centerlinesegments which are generated by splitting the (optionally corrected)centerline 3, 3′ at furcation points.

In order to get a homogeneous slice distance and to thus avoid imagedistortion, the centerline 3′ is first resampled into a resampledcenterline 3″ of a certain resolution (e.g. 0.1 mm) using, for instancea bicubic spline interpolation.

Then, for each point of the resampled centerline 3″, orthogonalcross-sections 9 (slices 9) of the volumetric data are extracted bycutting them with a plane that is centered on that point and spansperpendicular to the centerline direction of the resampled centerline3″. That means that for each centerline point of the resampledcenterline, an image slice 9 orthogonal to the resampled centerline 3″is interpolated with bi-linear interpolation at positions betweenvoxels.

These slices 9 are stored in a volume by parallelly stacking one on topof the other, which produces the warped volume data WID or warped imagedata WID. The size of each slice is preferably adjusted to the maximumexpected size of the extracted structure, i.e. it should at least coveran area which is big enough to show a cross-section 11 through the bloodvessel 1 with maximum diameter of the blood vessel 1. Since the diameterof coronary arteries does not exceed about 10 mm in size, the plane ofinterest in such case can safely be restricted to a size of 15 mm by 15mm. If other blood vessels are segmented, larger sizes may be appliedaccordingly.

As a result of the warping step W, the (resampled) centerline 3″ is astraight line in the warped image space and runs through the centre ofeach slice of the warped volume data WID. An advantage of thistransformation (warping) step W is that the lumen segmentation can nowbe performed in a cylindrical coordinate system which is particularlysuitable for tubular structures such as blood vessels.

Step V: Boundary Detection

The goal of the boundary detection step is to determine a (preliminary)boundary that separates the lumen of the blood vessel inside from itswall at each slice in the warped volume. To accomplish that, one firstneeds to find candidates at potential boundary positions and evaluatetheir suitability. In other words, boundary point candidates aregenerated and assigned a likelihood value.

It is advantageous to search for the lumen wall in polar, respectivelycylindrical, coordinates instead of using a Cartesian coordinate systembecause the detection of the lumen contour is reduced to a number ofsearches along a onedimensional ray. Such cylindrical coordinate systemis depicted in FIG. 4. Thereby, the height of a slice 9 in the warpedvolume is expressed by the coordinate z, whereas the angle k and theradial distance r determine a point in the cross-sectional plane (i.e.slice 9) in polar coordinates.

The following procedure is also known as a ray-casting method:considering the center of a slice—being the lumen center—to be a pole, adense radial sampling around the lumen center becomes feasible using asmall parameter space. FIG. 6 shows boundary candidate points generatedfor an equidistant selection of slices zε[1,Z] of the warped volume, forinstance for every slice or for every fifth slice (depending on thedesired accuracy). In each such slice R points (here: 5 points) along Krays are generated. Each of the points is thus defined by the slice, theangle k and the position 1 to 5 along its ray.

Each of such generated candidate boundary point is then evaluated forits likelihood to lie on the lumen boundary of the blood vessel. Forthat purpose different well-established models and methods areapplicable such as the weighted intensity differences method, thegradient magnitudes method or probability determination method based onpreviously trained classifier algorithms such as random forest orprobabilistic boosting tree algorithms. It is expected that they yield ahigher likelihood score at positions that are close to the lumenboundary. One can expect this boundary likelihood to be expressed as ascalar between 0 and 1. For convenience, the obtained likelihood valuesof the candidate boundary points can be stored in a volume l (k, z, r)of dimension K×Z×R, the boundary map B, as depicted in FIG. 6.

Each element in the boundary map should be a nonnegative value, thatyields only high values at positions close to the true lumen wall. Onecan hereby make use of the fact that tissue inside the lumen has ahigher intensity (e.g. HU−) value than outside the wall. That means,e.g. a large positive forward-difference calculated at successivepositions along a ray can be used to indicate a boundary. There are nowa number of possibilities to incorporate this into an algorithm. Two ofthe most obvious approaches are to either explicitly exploit derivativesto gain a lumen boundary score, or to use them implicitly, moreprecisely, to let a variety of derivative-features be evaluated byclassifiers in a machine learning approach to yield the soughtprobabilities.

Boundary detection against the background of machine learning iscommonly formulated as a binary classification problem. What is neededtherefore is some ground truth annotations, for instance from previousmanual segmentations supplied in a trained database: a trainedclassifier is used to predict the probability for a lumen wall beingpresent at each location given a feature sample. In order to train aclassifier, a set of correctly-classified observations has to be madeavailable to the classifier such that it can learn the distinguishingcharacteristics (features) from the observations. This is also referredto as supervised learning. That means, one has to provide two sets offeature data, one being evaluated at the true lumen wall (positive) andthe other one being computed distant from the boundary (negative). Afterthe training step, the classifier can be used to predict the boundaryprobability for any unseen feature sample and can thus be used forevaluation in the herein-described context of boundary likelihoodevaluation.

For every candidate boundary point at a location (k, z, r) theclassifier predicts whether (i.e. with which likelihood or probability)it is part of the lumen boundary of the blood vessel 1 or not. Itsprediction is based on low-level image features F(k, z, r) of the imagedata ID extracted from a local neighbourhood of the boundary candidatepoint in question, which is described in more detail with reference toFIG. 7:

For each candidate boundary point CBP, an image feature sampling patternSP is defined based on the point's CBP local orientation determined bythe line L connecting the centre point CP of the blood vessel in thecorresponding slice 9 and the potential (candidate) boundary point CBP.At each sampling position, low-level image features such as intensityand gradient are then computed. A binary classifier is then trainedbased on a representative set of manually segmented training data usingthese features to determine the likelihood/probability of the candidateboundary point CBP being on the blood vessel's boundary. Any binaryclassifier can be used such as the above-mentioned probabilisticboosting tree or random forest classifiers, which in tests bothdelivered results of similar high accuracy.

In training, for each orientation, the intersecting point 15 between theray and the ground truth annotation 11 is considered as positive and theremaining points 13 on the ray are considered negatives as shown in FIG.8 (left). FIG. 8 (right) shows the result of a boundary detectionprocess based on the classifier algorithm using the ground truth fromthe left in the form of a probability map output.

Step U: Calcium Exclusion

For a reliable lumen segmentation the correct handling of calcifiedplaque is mandatory especially when the boundary detection is in thebroadest sense based on image gradients. Due to the fact that calcium inCT images is characterized by high intensity values and is, hence, oftensimilar to intensities captured inside the lumen, it is oftenerroneously classified as lumen tissue and boundaries are detectedbetween plaque and vessel back-ground rather than lumen and plaque.However, calcified regions in coronary arteries indicatelife-threatening stenoses and are per definition not part of theblood-flowed lumen and therefore, have to be excluded from thesegmentation results. For that purpose, boundaries are to be detectedbetween (calcified) plaque and the blood vessel lumen rather thanbetween (calcified) plaque and the blood vessel background.

In order to comprehend why calcified plaque is erroneously included inthe segmentation, the inventors analyzed the radial profile ofintensity, lumen probability and boundary probability values forabnormalities. Their profile exhibits a certain pattern when thecorresponding ray is passing through a calcified region instead of ahealthy one.

FIGS. 9 and 10 show on top the same cross-sectional view of a bloodvessel. In FIG. 9 a ray 17 through a healthy part of the blood vessel isshown, whereas in FIG. 10 a ray 17′ in a different direction within thesame blood vessel passes through calcified plaque which can bedistinguished by the lightness of the picture in the region of theplaque. On the bottom diagrammes of the two figures, profiles for theimage intensity JJ, the lumen likelihood LL (cf. step X) and theboundary likelihood (cf. step V) have been extracted for a slice and aparticular ray at a given angle such as the two different rays 17, 17′in the two figures. The horizontal axis shows a distance d in mm whereasthe vertical axis refers to a likelihood L in numbers between 1 and 0and to an intensity J without numbers given but with a set zerothreshold level which corresponds to a CT image intensity of 576 HU

As for FIG. 9, the image intensity JJ is always below the set thresholdlevel. Whilst the lumen likelihood from left to right shows acomparatively steady curve downwards to zero, the boundary likelihoodshows essentially one peak at about position 1.3 mm.

As for FIG. 10, the image intensity exceeds the set threshold level atabout a distance of 1.5 mm, reaching a peak value at about 2.2 mm andgoing below the set threshold level at about 2.7 mm. The lumenlikelihood LL shows two peaks and the boundary likelihood BL shows eventhree peaks, the leftmost of which corresponds to the true lumenboundary which excludes the calcified plaque. The rightmost peak of theboundary likelihood BL refers to a boundary that erroneously includesthe calcified plaque. A corrected boundary likelihood l_(c) correspondsto the true boundary likelihood which excludes the calcified plaque.This is accomplished in a heuristic approach as follows:

First, the calcified plaque is identified by determining the ranges ofthe intensity profile that are above a certain predefined threshold,here the set threshold of 576 HU. In order to increase robustness andprevent false responses the threshold can be raised dependent on thecurrent image data by adding to it (or reducing it by) an image datadependent variance (preferably twice such variance), based on lumenintensity distribution (cf. step X). The set threshold t_(CAL) can thusbe a chosen constant or an adaptive one using a fixed threshold t_(f)and the mean lumen intensity μ₁ plus twice its variance σ₁ so thatt _(CAL)=max(t _(f),μ₁+2σ₁)  (1)

Then, the range along the ray 17′ which is closest to the centerline andwhich preferably has a certain minimum length of e.g. 0.3 mm is regardedas the relevant calcified range. In addition to the index of thestarting radius r₀ at the centerline point there is also extracted theradius r_(m) for which the intensity is maximal within the calcifiedrange (that is the peak of the image intensity JJ at about 2.2 mm inFIG. 11). Then, the corrected boundary likelihood l_(c) along the ray17′ is obtained as

$\begin{matrix}{{l_{c}( {k,z,r} )} = \{ \begin{matrix}{l( {k,z,r} )} & {r < r_{0}} \\{{l( {k,z,r} )} \cdot d_{CAL}^{{{({r - r_{0}})}/\Delta}\; r}} & {r_{0} \leq r < r_{m}} \\0 & {r \geq r_{m}}\end{matrix} } & (2)\end{matrix}$where Δ_(r) is the radial sampling resolution (e.g. Δ_(r)=0.1 mm) andd_(CAL) is a damping factor which determines the speed of decay of theboundary likelihood profile between r₀ and r_(m). For instance, d_(CAL)can be set as 0.6.

As can be seen in FIG. 10, this strategy leads to a corrected boundarylikelihood profile with only one peak which describes a boundary whichcorrectly excludes the calcified plaque.

It may be noted that after the correction of the boundary likelihoods ofthe blood vessel, it is possible to re-correct the progression line(centerline) as proposed in step X because the lumen of the modelledblood vessel may have changed considerably.

Step T: Segmentation

In the last step, optimal boundaries of the blood vessel are found fromthe corrected boundary map. In addition to the (corrected) boundarylikelihood, 3D smoothness constraints can be considered to avoidunsteady contours and to accomplish a smooth surface. This problem canbe formulated in a first order Markov Random Field (MRF) with discretemultivariate random variables. The problem of finding an optimalsegmentation can then be regarded as a maximum a posteriori (MAP)estimation in this MRF for which an efficient solver based on themax-flow algorithm has been proposed by Ishikawa, Hiroshi: ExactOptimization for Markov Random Fields with Convex Priors. IEEETransactions on Pattern Analysis and Machine Intelligence. Vol 25, No.10, pp. 1333-1336. This reference is explicitly considered part of theteachings of this description.

More formally (cf. FIG. 11), a graph G=(V,E) is defined with a set ofvertices V and a set of undirected edges E∪V×V. A MRF includes a graphG, a finite set of labels L={l₁, . . . l_(R)} and a probabilitydistribution P on the space of potential label assignments X=L^(v) whichis the amount of all labels L. Each label thus refers to a (candidate)position along the ray normal to the initial surface model of the bloodvessel at the position of the vertex. Thereby, a normal can beconsidered to be the mean normal of normals of the adjacent meshsurfaces of the position of the vertex.

An element XεX, which can also be considered a configuration, is a mapthat assigns each vertex v a label X_(v) in L. As is known from theabove reference of Ishikawa, one can effectively minimize multi-labelenergy functions of the form

$\begin{matrix}{{E(X)} = {{\sum\limits_{{({u,v})} \in E}^{\;}\;{\gamma_{uv}{g( {X_{u} - X_{v}} )}}} + {\sum\limits_{v \in V}^{\;}\;{h( {v,X_{v}} )}}}} & (3)\end{matrix}$where g(·) is a convex function weighting the label difference of vertexu and vertex v. γ_(uv) is a predefined smoothness factor which will beexplained below.

The first of the above-given sums can be referred as prior as it is datadependent, whereas the second of these sums can be called a data term asit incorporates the observations (i.e. the boundary likelihood in thiscase). Energy functions of this form can be converted into an equivalentgraph-cut problem which can be solved exactly within polynomial time bya min-cut/max-flow algorithm of which there are several variantsavailable.

The segmentation problem is formulated as an MRF as follows: Each vertexv of the MRF corresponds to a mesh vertex of the tubular mesh (cf. FIG.11) which is denoted by an angle (or ray number) k and a height z.

The associated random variable X_(k,z) is a multivariate, takes aninteger value r in the range of [1 . . . R] (corresponding to the labelset L={l₁ . . . l_(R)}) and represents the event that the surface goesthrough the boundary candidate at height z, and angle k and a radius r.The data term of equation (3) is then defined ash(v,X_(v))=h(X_(k,z))=−log(l(r,k,z)), the negative logarithmiclikelihood (negative in order to be able reduce the energy function ofequation (3) with increasing likelihood) of the boundary candidatescomputed on the previous step U. It may be noted in this context thatlog(l(r,k,z)) may also refer to log(l_(c)(r,k,z)), i.e. to the correctedboundary likelihood after the calcium exclusion step. While for theprior term (the smoothness term) in equation (3) an arbitrary convexfunction g(·) can be chosen, three types of functions are particularlywell-suited:

$\begin{matrix}{{g(d)} = {\beta{d}( {L\; 1\mspace{14mu}{norm}} )}} & (4) \\{{g(d)} = {\beta\{ {\begin{matrix}0 & {{d} \leq \alpha} \\( {{d} - \alpha} ) & {{d} > \alpha}\end{matrix}( {ɛ - {insensitive}} )} }} & (5) \\{{g(d)} = {\beta\{ {\begin{matrix}( {d/\alpha} ) & {{d} \leq \alpha} \\{{2{{d/\alpha}}} - 1} & {{d} > \alpha}\end{matrix}( {{Huber}\mspace{14mu}{function}} )} }} & (6)\end{matrix}$where d=X_(u)−X_(v) is the difference between two integer labels betweenvariables X_(u) and X_(v) that are neighbours U,VεE_(G) in the MRFgraph. The functions are parameterized through a threshold parameter αand a slope parameter β. The corresponding curves C₁ for equation (4),C₂ for equation (6) and C₃ for equation (5) are depicted in FIG. 12.While equation (6) can be considered to deliver the most preciseresults, results from equation (4) can be computed fastest and equation(5) lies in the middle between both these functions with respect tospeed and precision.

Given the MRF represented by the undirected graph G and the definedpotentials, a graph-cut problem is formulated for minimizing equation(3). To this end, a directed graph H is constructed with KZR+2 verticesand directed edges u,vεE_(H) that are associated with positivecapacities c(u,v)>0. The graph is constructed in a way that every σ−τcut in H (i.e. a cut that separates a source σ and a sink τ−cf. FIG. 13)corresponds to a configuration (i.e. to a variable assignment) XεX ofthe MRF G and the cost of the cut (i.e. the sum of the capacities c(u,v)of the edges of H that are in the cut) is the cost of this configurationaccording to equation (3) (cf. FIG. 13). Pseudo-code for generating thegraph H is provided in algorithms (1), (2), and (3), where H.addCapacity(u, v, a, b) adds the capacities a and b to the two directed edgesbetween u and v, i.e. c(u,v)=c(u,v)+a and c(v,u)=c(v,u)+b.

Algorithm 1: Graph construction - data term input: boundary map l(k, z,r) of dimension K × Z × R output: graph H with data term capacities /*add data terms for k ← 1 to K do | for z ← 1 to Z do | | H.addCapacity(σ, V_(k,z,1), ∞, 0) ; | | for r ← 1 to R − 1 do | | | H.addCapacity(V_(k,z,r), V_(k,z,r+1), −log(l(k, z, r)) , ∞); | | H.addCapacity(V_(k,z,R), τ, −log(l(k, z, R)), 0)

Algorithm 2: Graph construction - smoothness term input: smoothnessweight factors Υ_(z) and Υ_(k) parameters: Dimension K, Z, R of theproblem output: graph H with smoothness term capacities /* addsmoothness terms between slices for k ← 1 to K do | for z ← 1 to Z − 1do | | addPairPotential (H, k, z, k, z+1, Υ_(z) /* add smoothness termsbetween rays for z ← 1 to Z do | for k ← 1 to K − 1 do | |addPairPotential (H, k, z, k+1, z, Υ_(k)) | addPairPotential (H, K, z,1, z, Υ_(k))

Algorithm 3: Graph construction - addPairPotential (H, k₀, z₀, k₁, z₁,Υ) input: H, k₀, z₀, k₁, z₁, Υ parameters: Dimension K, Z, R of theproblem output: graph H with modified capacities for d ← 0 to R do | ifc(d)>0 then | | c = Υ cap(d); /* see equation (7) below */ | | if d = 0then | | | c = c/2 /* added twice to the same edge for d = 0 */ | | forr ← 1 to R−d do | | | H.addCapacity (V_(k0,z0,r), V_(k1,z1,r+d), c, c);| | | H.addCapacity (V_(k1,z1,r), V_(k0,z0,r+d), c, c); | | for r ← 1 tod−1 do | | | H.addCapacity (V_(k0,z0,1), V_(k1,z1,d−r) c, c); | | |H.addCapacity (V_(k1,z1,1), V_(k0,z0,d−r), c, c); | | for r ← 0 to d−1do | | | H.addCapacity (V_(k0,z0,R−r), R−r, τ, c, c); | | |H.addCapacity (V_(k1,z1,R−r), R−r, τ, c, c);

Besides the two distinguished vertices σ and τ, each vertex in Hcorresponds to a variable assignment X_(k,z)=r and is thus denoted byV_(k,z,r). Capacities representing the data term

$\sum\limits_{v \in V}^{\;}\;{h( {v,X_{v}} )}$from equation (3) are added to the edges between V_(k,z,r) andV_(k,z,r+1) as H.addCapacity (V_(k,z,r),V_(k,z,r+1),−log(l(r.k.z)),∞)and to the edges (π,V_(k,z,l)) and (V_(k,z,R),τ) as shown in algorithm(1).

Capacities representing MRF pair potentials γ_(uv)g(X_(u)−X_(v)) fromequation (3) are constructed from each edge from the MRF graph G (cf.algorithm (2)). Between the variables X_(k,z) and X_(k,z+1) ofneighbouring slices a smoothness factor γ_(uv)=γ_(k) is used. Each pairpotential may require to add several capacities to the graph H (cf.algorithm (3)) which are computed as second-order differences from thechosen pair-potential functions (cf. equations (4) to (6)) as

$\begin{matrix}{{{cap}(d)} = \frac{{g( {d + 1} )} - {2\;{g(d)}} + {g( {d - 1} )}}{2}} & (7)\end{matrix}$

Here, d=r₁−r₀ is the label difference between the connected variablesX_(k1,z1)=r₁ and X_(k0,z0)=r₀, i.e. the vertices V_(k1,z1,r1) andV_(k0,z0,r0) in H. Thereby, cap(d)=0 for label distances d where thepair-potential function g(d) is linear and that for these vertices noedges in H are created. Thus, the resulting graph is sparser forpair-potential functions with linear parts, such as equations (4) to(6), which ultimately results in a faster computation of themin-cut/max-flow solution.

Finally, it needs to be stated that any min-cut/max-flow algorithm canbe used to obtain the minimum solution of equation (3) which is theconfiguration X that corresponds to the minimum cut.

Although the present invention has been disclosed in the form ofpreferred embodiments and variations thereon, it will be understood thatnumerous additional modifications and variations could be made theretowithout departing from the scope of the invention.

For the sake of clarity, it is to be understood that the use of ‘a’ or‘an’ throughout this application does not exclude a plurality, and‘comprising’ does not exclude other steps or elements.

The patent claims filed with the application are formulation proposalswithout prejudice for obtaining more extensive patent protection. Theapplicant reserves the right to claim even further combinations offeatures previously disclosed only in the description and/or drawings.

The example embodiment or each example embodiment should not beunderstood as a restriction of the invention. Rather, numerousvariations and modifications are possible in the context of the presentdisclosure, in particular those variants and combinations which can beinferred by the person skilled in the art with regard to achieving theobject for example by combination or modification of individual featuresor elements or method steps that are described in connection with thegeneral or specific part of the description and are contained in theclaims and/or the drawings, and, by way of combinable features, lead toa new subject matter or to new method steps or sequences of methodsteps, including insofar as they concern production, testing andoperating methods.

References back that are used in dependent claims indicate the furtherembodiment of the subject matter of the main claim by way of thefeatures of the respective dependent claim; they should not beunderstood as dispensing with obtaining independent protection of thesubject matter for the combinations of features in the referred-backdependent claims. Furthermore, with regard to interpreting the claims,where a feature is concretized in more specific detail in a subordinateclaim, it should be assumed that such a restriction is not present inthe respective preceding claims.

Since the subject matter of the dependent claims in relation to theprior art on the priority date may form separate and independentinventions, the applicant reserves the right to make them the subjectmatter of independent claims or divisional declarations. They mayfurthermore also contain independent inventions which have aconfiguration that is independent of the subject matters of thepreceding dependent claims.

Further, elements and/or features of different example embodiments maybe combined with each other and/or substituted for each other within thescope of this disclosure and appended claims.

Still further, any one of the above-described and other example featuresof the present invention may be embodied in the form of an apparatus,method, system, computer program, tangible computer readable medium andtangible computer program product. For example, of the aforementionedmethods may be embodied in the form of a system or device, including,but not limited to, any of the structure for performing the methodologyillustrated in the drawings.

Even further, any of the aforementioned methods may be embodied in theform of a program. The program may be stored on a tangible computerreadable medium and is adapted to perform any one of the aforementionedmethods when run on a computer device (a device including a processor).Thus, the tangible storage medium or tangible computer readable medium,is adapted to store information and is adapted to interact with a dataprocessing facility or computer device to execute the program of any ofthe above mentioned embodiments and/or to perform the method of any ofthe above mentioned embodiments.

The tangible computer readable medium or tangible storage medium may bea built-in medium installed inside a computer device main body or aremovable tangible medium arranged so that it can be separated from thecomputer device main body. Examples of the built-in tangible mediuminclude, but are not limited to, rewriteable non-volatile memories, suchas ROMs and flash memories, and hard disks. Examples of the removabletangible medium include, but are not limited to, optical storage mediasuch as CD-ROMs and DVDs; magneto-optical storage media, such as MOs;magnetism storage media, including but not limited to floppy disks(trademark), cassette tapes, and removable hard disks; media with abuilt-in rewriteable non-volatile memory, including but not limited tomemory cards; and media with a built-in ROM, including but not limitedto ROM cassettes; etc. Furthermore, various information regarding storedimages, for example, property information, may be stored in any otherform, or it may be provided in other ways.

Although the invention has been illustrated and described in detail onthe basis of the preferred example embodiment, the invention is notlimited by the disclosed examples and other variations can be derivedherefrom by the person skilled in the art, without departing from thescope of protection of the invention.

What is claimed is:
 1. A method for segmentation of a biologicalstructure, in image data, comprising: providing an image representationof the biological structure; providing a start surface model, includinga mesh with a plurality of vertices connected by edges; defining foreach vertex a ray normal to the surface model at the position of thevertex; assigning more than two labels to each vertex, each labelrepresenting a candidate position of the vertex on the ray; providing arepresentation of likelihoods for each candidate position, thelikelihood referring to whether the candidate position corresponds to asurface point of the biological structure in the image representation;defining a first order Markov Random Field with discrete multivariaterandom variables, the random variables including the labels of thecandidate positions and the representation of likelihoods; andsegmenting the image representation of the biological structure, thesegmenting including, determining a selected segmentation of thebiological structure using an maximum a posteriori estimation in theMarkov Random Field, the selected segmentation representing a truesurface of the biological structure.
 2. The method of claim 1, wherein amax-flow algorithm is used in the maximum a posteriori estimation. 3.The method of claim 1, wherein a multi-label energy function isminimized for the maximum a posteriori estimation.
 4. The method ofclaim 3, wherein the multi-label energy function comprises a likelihoodfunction part representing a sum of all likelihoods for the differentvertices and their labels of their candidate positions.
 5. The method ofclaim 3, wherein the multi-label energy function comprises a smoothnessfunction part representing a smoothness of the segmentation.
 6. Themethod of claim 5, wherein the smoothness function part comprises a sum,for all edges, over function values of a convex function, the convexfunction depending on a label difference of the labels connected by eachedge.
 7. The method of claim 5, wherein the smoothness function partcomprises an edge dependent weighting factor.
 8. The method of claim 4,wherein the likelihood function part is based on a pre-given boundarylikelihood of the image representation of the biological structure. 9.The method of claim 5, wherein the likelihood function part is based ona pre-given boundary likelihood of the image representation of thebiological structure.
 10. The method of claim 8, wherein the biologicalstructure includes at least a calcified blood vessel and the boundarylikelihood is a corrected boundary likelihood derived by at least thefollowing: providing a vesseltree representation of the blood vessel;providing a number of preliminary boundary likelihoods of a number ofcross-sections of the blood vessel; providing a number of intensityprofiles in the image data in the number of cross-sections; determininga calcification in the cross-section based on the intensity profile; andcorrecting each preliminary boundary likelihood into the correctedboundary likelihood which excludes the calcification from an inner partof the blood vessel.
 11. The method according to claim 9, wherein thebiological structure includes at least a calcified blood vessel and theboundary likelihood is a corrected boundary likelihood derived by atleast the following: providing a vesseltree representation of the bloodvessel; providing a number of preliminary boundary likelihoods of anumber of cross-sections of the blood vessel; providing a number ofintensity profiles in the image data in the number of cross-sections;determining a calcification in the cross-section based on the intensityprofile; and correcting each preliminary boundary likelihood into thecorrected boundary likelihood which excludes the calcification from aninner part of the blood vessel.
 12. A segmentation system forsegmentation of a biological structure, in image data, comprising: amemory configured to store instructions; and a processor configured toexecute the instructions such that the processor is configured to,provide an image representation of the biological structure, provide astart surface model, comprising a mesh with a plurality of verticesconnected by edges, define, for each vertex, a ray normal to the surfacemodel at the position of the vertex, assign more than two labels to eachvertex, each label representing a candidate position of the vertex onthe ray, provide a representation of likelihoods for each candidateposition the likelihood referring to whether the candidate positioncorresponds to a surface point of the biological structure in the imagerepresentation, define a first order Markov Random Field with discretemultivariate random variables, the random variables comprising thelabels of the candidate positions and the representation of likelihoods,and segment the image representation of the biological structureincluding, determine a selected segmentation of the biological structureby using an maximum a posteriori estimation in the Markov Random Field,the selected segmentation representing a true surface of the biologicalstructure.
 13. A tomographic imaging device comprising: an acquisitionunit; and the segmentation system of claim
 12. 14. A non-transitorycomputer readable medium including computer readable instructions, whenexecuted by a programmable segmentation system, causing the programmablesegmentation system to implement the method of claim
 1. 15. Anon-transitory computer readable medium including computer readableinstructions, when executed by a programmable segmentation system,causing the programmable segmentation system to implement the method ofclaim
 8. 16. A non-transitory computer readable medium includingcomputer readable instructions, when executed by a programmablesegmentation system, causing the programmable segmentation system toimplement the method of claim 9.